Convergence Analysis of Projection Methods for the Numerical Solution of Large Lyapunov Equations

Authors:
V. Simoncini;V. Druskin
Affiliations:
valeria@dm.unibo.it;-
Venue:
SIAM Journal on Numerical Analysis
Year:
2009

Citing 0
Cited 5

Krylov Subspace Methods for Linear Systems with Tensor Product Structure

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Inverse Iteration for Purely Imaginary Eigenvalues with Application to the Detection of Hopf Bifurcations in Large-Scale Problems

SIAM Journal on Matrix Analysis and Applications
Krylov subspace methods for projected Lyapunov equations

Applied Numerical Mathematics
Analysis of the Rational Krylov Subspace and ADI Methods for Solving the Lyapunov Equation

SIAM Journal on Numerical Analysis
An Error Analysis for Rational Galerkin Projection Applied to the Sylvester Equation

SIAM Journal on Numerical Analysis

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Abstract

The numerical solution of large-scale continuous-time Lyapunov matrix equations is of great importance in many application areas. Assuming that the coefficient matrix is positive definite, but not necessarily symmetric, in this paper we analyze the convergence of projection-type methods for approximating the solution matrix. Under suitable hypotheses on the coefficient matrix, we provide new asymptotic estimates for the error matrix when a Galerkin method is used in a Krylov subspace. Numerical experiments confirm the good behavior of our upper bounds when linear convergence of the solver is observed.